#pragma GCC optimize ("O3") #include "bits/stdc++.h" using namespace std; using ll = long long int; #define debugos cout #define debug(v) {printf("L%d %s > ",__LINE__,#v);debugos<<(v)< ",__LINE__,#v);for(auto e:(v)){debugos< ",__LINE__,#m);for(int x=0;x<(w);x++){debugos<<(m)[x]<<" ";}debugos<\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){debugos<<(m)[y][x]<<" ";}debugos< f) { if (!assertion) { cerr << "assertion fault:" << endl; f(); abort(); } } template inline ostream& operator <<(ostream &o, const pair p) { o << '(' << p.first << ':' << p.second << ')'; return o; } template inline ostream& _ostream_vecprint(ostream& os, const Vec& a) { os << '['; for (const auto& e : a) os << ' ' << e << ' '; os << ']'; return os; } template inline ostream& operator<<(ostream& o, const vector& v) { return _ostream_vecprint(o, v); } template inline ostream& operator<<(ostream& o, const array& v) { return _ostream_vecprint(o, v); } template inline T& chmax(T& to, const T& val) { return to = max(to, val); } template inline T& chmin(T& to, const T& val) { return to = min(to, val); } void bye(string s, int code = 0) { cout << s << endl; exit(code); } mt19937_64 randdev(8901016); template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_int_distribution(l, h)(rand); } template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_real_distribution(l, h)(rand); } #if defined(_WIN32) || defined(_WIN64) #define getchar_unlocked _getchar_nolock #define putchar_unlocked _putchar_nolock #elif defined(__GNUC__) #else #define getchar_unlocked getchar #define putchar_unlocked putchar #endif namespace { #define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E) class MaiScanner { public: template void input_integer(T& var) noexcept { var = 0; T sign = 1; int cc = getchar_unlocked(); for (; cc<'0' || '9'>(int& var) noexcept { input_integer(var); return *this; } inline MaiScanner& operator>>(long long& var) noexcept { input_integer(var); return *this; } inline MaiScanner& operator>>(string& var) { int cc = getchar_unlocked(); for (; !isvisiblechar(cc); cc = getchar_unlocked()); for (; isvisiblechar(cc); cc = getchar_unlocked()) var.push_back(cc); return *this; } template inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; } }; class MaiPrinter { public: template void output_integer(T var) noexcept { if (var == 0) { putchar_unlocked('0'); return; } if (var < 0) putchar_unlocked('-'), var = -var; char stack[32]; int stack_p = 0; while (var) stack[stack_p++] = '0' + (var % 10), var /= 10; while (stack_p) putchar_unlocked(stack[--stack_p]); } inline MaiPrinter& operator<<(char c) noexcept { putchar_unlocked(c); return *this; } inline MaiPrinter& operator<<(int var) noexcept { output_integer(var); return *this; } inline MaiPrinter& operator<<(long long var) noexcept { output_integer(var); return *this; } inline MaiPrinter& operator<<(char* str_p) noexcept { while (*str_p) putchar_unlocked(*(str_p++)); return *this; } inline MaiPrinter& operator<<(const string& str) { const char* p = str.c_str(); const char* l = p + str.size(); while (p < l) putchar_unlocked(*p++); return *this; } template void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this <<* begin; } }; } MaiScanner scanner; MaiPrinter printer; class llmod { private: using value_type = long long; value_type val_; // inline ll cut(ll v) const { return ((v%MOD) + MOD) % MOD; } // safe public: static const value_type MOD = MD; // <= llmod() : val_(0) {} llmod(value_type num) :val_(((num % MOD) + MOD) % MOD) {} inline operator value_type() const { return val_; } inline value_type operator *() const { return val_; } inline llmod& operator=(const llmod& lm) { val_ = lm.val_; return *this; } inline llmod& operator=(value_type v) { val_ = (v) % MOD; return *this; } inline llmod& operator+=(value_type v) { val_ = (val_ + v) % MOD; return *this; } inline llmod& operator+=(const llmod& l) { val_ = (val_ + l.val_) % MOD; return *this; } inline llmod& operator-=(value_type v) { val_ = (val_ - v + MOD) % MOD; return *this; } inline llmod& operator-=(const llmod& l) { val_ = (val_ - l.val_ + MOD) % MOD; return *this; } inline llmod& operator*=(value_type v) { val_ = (val_ * v) % MOD; return *this; } inline llmod& operator*=(const llmod& l) { val_ = (val_ * l.val_) % MOD; return *this; } inline llmod& operator++() { val_ = (val_ + 1) % MOD; return *this; } inline llmod operator++(int) { llmod t = *this; val_ = (val_ + 1) % MOD; return t; } inline llmod& justify() { val_ = ((val_ % MOD) + MOD) % MOD; return *this; } friend llmod pow(llmod, long long); }; inline ostream& operator<<(ostream& os, const llmod& l) { os << *l; return os; } inline llmod operator+(llmod t, const llmod& r) { return t += r; } inline llmod operator-(llmod t, const llmod& r) { return t -= r; } inline llmod operator*(llmod t, const llmod& r) { return t *= r; } // MEMO : 逆元...pow(n,MD-2) llmod pow(llmod x, long long p) { llmod::value_type y = 1; llmod::value_type xval = x.justify(); while (0 < p) { if (p & 1) y = (xval * y) % llmod::MOD; xval = (xval * xval) % llmod::MOD; p >>= 1; } return llmod(y); } inline llmod& operator/=(llmod& l, const llmod& r) { return l *= pow(r, llmod::MOD - 2); } template // using T = double; class Matrix { public: size_t height_, width_; valarray data_; Matrix(size_t height = 1, size_t width = 1) :height_(height), width_(width), data_(height*width) {} template Matrix(size_t height, size_t width, const V& data) : height_(height), width_(width), data_(data) {} Matrix(size_t height, size_t width, initializer_list init) : height_(height), width_(width), data_(init) {} inline T& operator()(size_t y, size_t x) { return data_[y*width_ + x]; } inline T operator() (size_t y, size_t x) const { return data_[y*width_ + x]; } inline T& at(size_t y, size_t x) { return data_[y*width_ + x]; } inline T at(size_t y, size_t x) const { return data_[y*width_ + x]; } inline void resize(size_t h, size_t w) { height_ = h; width_ = w; data_.resize(h*w); } inline void resize(size_t h, size_t w, T val) { height_ = h; width_ = w; data_.resize(h*w, val); } inline void fill(T val) { data_ = val; } Matrix& setDiag(T val) { for (size_t i = 0, en = min(width_, height_); i < en; ++i)at(i, i) = val; return *this; } void print(ostream& os) { os << "- - -" << endl; // << setprecision(3) for (size_t y = 0; y < height_; ++y) { for (size_t x = 0; x < width_; ++x) { os << setw(7) << at(y, x) << ' '; }os << endl; } } }; template inline ostream& operator << (ostream& os, Matrix mat) { mat.print(os); return os; } template Matrix multiply(const Matrix& mat1, const Matrix& mat2) { assert(mat1.width_ == mat2.height_); Matrix result(mat1.height_, mat2.width_); for (size_t i = 0; i < mat1.height_; ++i) for (size_t j = 0; j < mat2.width_; ++j) for (size_t k = 0; k < mat1.width_; ++k) result(i, j) += mat1(i, k) * mat2(k, j); return result; } template V multiply(const Matrix& mat1, const V& vec2) { assert(mat1.width_ == vec2.size()); V result(mat1.height_); for (size_t i = 0, j; i < mat1.height_; ++i) for (j = 0; j < mat1.width_; ++j) result[i] += mat1(i, j) * vec2[j]; return result; } template inline Matrix& operator+=(Matrix& mat, T val) { mat.data_ += val; return mat; } template inline Matrix& operator-=(Matrix& mat, T val) { mat.data_ -= val; return mat; } template inline Matrix& operator*=(Matrix& mat, T val) { mat.data_ *= val; return mat; } template inline Matrix& operator/=(Matrix& mat, T val) { mat.data_ /= val; return mat; } template inline Matrix& operator^=(Matrix& mat, T val) { mat.data_ ^= val; return mat; } template inline Matrix& operator+=(Matrix& mat1, const Matrix& mat2) { mat1.data_ += mat2.data_; return mat1; } template inline Matrix operator+(Matrix& mat1, const Matrix& mat2) { return Matrix(mat1.height_, mat1.width_, mat1.data_ + mat2.data_); } template inline Matrix& operator-=(Matrix& mat1, const Matrix& mat2) { mat1.data_ -= mat2.data_; return mat1; } template inline Matrix operator-(Matrix& mat1, const Matrix& mat2) { return Matrix(mat1.height_, mat1.width_, mat1.data_ - mat2.data_); } template inline Matrix& operator*=(Matrix& mat1, const Matrix& mat2) { mat1 = multiply(mat1, mat2); return mat1; } template inline Matrix operator*(const Matrix& mat1, const Matrix& mat2) { return multiply(mat1, mat2); } template inline V operator*(const Matrix& mat1, const V& vec2) { return multiply(mat1, vec2); } template Matrix pow(Matrix a, long long p) { assert(a.height_ == a.width_); Matrix b(a.height_, a.height_); b.setDiag(1); while (0 < p) { if (p & 1) b *= a; a *= a; p >>= 1; } return b; } int main(){ Matrix mat(2,2, { 10, 1, 0, 1 }); ll N; scanner >> N; auto m2 = pow(mat, N); Matrix vec(2, 1, { 1, 3 }); auto v = m2*vec; cout << v(0, 0) << endl; return 0; }